MODEL ANGULAR MOMENTUM

For more information on Angular Momentum see here]

Given a particle with momentum p = m v. The angular momentum (L) of this particle about a distal point is: L= r x p

The center of mass of an object is a theoretical point where all of the object’s mass can be considered to be concentrated Compute the Center of Mass of the model from the location of the center of mass of each segment. Total Mass of the Model Location of the center of mass of the model.

Vector from the COM of the Model to the COM of a segment. (e.g. Red vector in the figure above)

Velocity of a Segment COM relative to the laboratory Velocity of the Model COM relative to the laboratory Velocity of a vector from the Segment COM to the Model COM in Laboratory coordinates.

Compute in Local Coordinates = Segment angular velocity in Lab Coordinates = Segment orientation matrix, which transforms a vector from Lab coordinates to Local coordinates Compute the segment angular velocity in Segment Local Coordinates = Segment Angular Momentum in Local Coordinates

Segment Angular Momentum in Lab Coordinates

The angular momentum for one segment about the total body center of mass in Laboratory Coordinates is:

Now that all the angular moment values in a common coordinate system, we can simply add them. The angular momentum for the total body about the total body center of mass is: Where N = total number of segments Note: The tricky calculation is so the algorithm works around this issue by not actually calculating the value.

Much of the contents of this page are courtesy of Fred Yeadon.

Yeadon, M.R. 1993. The biomechanics of twisting somersaults. Part I: Rigid body motions. Journal of Sports Sciences 11, 187-198.

Yeadon, M.R. 1993. The biomechanics of twisting somersaults. Part II: Contact twist. Journal of Sports Sciences 11, 199-208.

Yeadon, M.R. 1993. The biomechanics of twisting somersaults. Part III: Aerial twist. Journal of Sports Sciences 11, 209-218.

Yeadon, M.R. 1993. The biomechanics of twisting somersaults. Part IV: Partitioning performance using the tilt angle. Journal of Sports Sciences 11, 219-225.

Yeadon, M.R. 1993. Twisting techniques used by competitive divers. Journal of Sports Sciences 11, 4, 337-342.